The role of math in physics more or less

I have hear it said that math is the "queen of physics". In the past the only person more powerful than the King was the Queen. Newton came up with the theory of gravity as a result of observation. So as the queens supports her king the math supports the king. Now there's a lot of people trying to adjust their explanation of the universe to the consequences of equations, math etc...I am new to this forum so I will stop with this for now but I am looking forward to how people feel that trying to adjust the universe to fit established equations could be a major obstacle to breakthrough ideas. Am I alone in this thought?

Staff: Mentor

Welcome to PF!

The universe doesn't care how we want it to work and won't let us change it. If a person tries to "adjust the universe", the universe will simply not allow it and the math won't be an accurate description of reality.

As far as that being an obstacle, sure: attempting to bend the universe to the scientist's will would be a waste of time and therefore an obstacle to understanding how the universe works. So that's why they try to avoid doing that.

It is not a matter of fitting reality to established equations, but rather finding equations that fit reality. Equations do not "limit" ideas, they allow ideas to be expressed precisely. Some are encountered more often than others, and are easier to work with, so they are prefered. But their limits are always, or should always be, kept in mind. In practice, more than anything, they have to be usable.

Faraday was not fortunate to learn much mathematics,so he brilliantly made excessive use of field lines to express his ideas.Later Maxwell put those ideas in the form of four famous and beautiful differential equations.
In explaining intricacies of quantum world such mathematical ideas like group theory were used which earlier seemed only mathematical adventures.

The fact that physical processes are so readily describable through mathematics should not be surprising at all. The characteristics of physical entities and actions are numeric by their nature... quantity, shape, size, magnitude, velocity, with dynamical changes through accelerations, rotations, wave mechanics, ect. The objective descriptions of these entities and actions will, of course, be representable mathematically. The miraculous part of this has been our recognition of these mathematical patterns and the intellectual progress as a result of that.

May be he could advance but in a cumbersome,tedious and exhausting way.
Whenever we do any daily life work we are may be unknowingly using mathematics.
A scientist goes more advanced since after all he is also dealing with physical world.

Experimental physics is about measuring or finding numbers in nature, theoretical physics is about finding relations between these measurments. Math can be seen as a nothing more than a set of abbreviations for certain words that are often used. Mental short cuts, since using English or any common language would be too cumbersome. That's all it really is.

Maybe it would help if you think of mathematics as simply being a specific type of logic. Physics is all about logical relationships between observable entities and events. If you accept, as Leibniz argues, that all of physical existence is relational and that all physical events happen for a reason, then the job of the physicist is to recognize the patterns in those physical events and theorize about the "reason" for them.
Mathematics provides the logical framework to OBJECTIVELY define the relationships between the physical entities and actions that are observable... which then enables the "if this, then that" testable types of hypotheses that are the hallmark of the scientific process.
So, this process helped Newton build on the concepts already developed by Copernicus and Kepler (among others). His abstract thought about the nature of gravity might be considered somewhat "philosophical" in nature. But what provided the scientific breakthrough was the way that he used "the calculus" to describe the gravitational "force" with precision, which then was able to be verified by observation and experimentation.
Mathematics (and other forms of logical representation) is simply the language that "objectively" describes the physical qualities of existence that are observable. This connection between physics and mathematics is relatively clear cut and self evident. The far more confusing (and admittedly philosophical) questions arise when one starts to question whether the mathematics/logic does not simply "describe" reality, but rather, it IS reality... in the sense that the INFORMATION is all that really exists. But that discussion is for a different thread.

Maybe it would help if you think of mathematics as simply being a specific type of logic.

Or maybe it would help more to think of logic as a specific kind of maths.

Mathematics is a language. It has symbols with meanings and operations by which it is correct (one might call it grammatically correct) to manipulate those symbols. A part of how this language, some of some forms of it, was created was in selecting language rules that correspond to our observations.

Is it then miraculous that the universe follows mathematical rules? Well... Maybe.